The present invention particularly relates to an interference measuring device belonging to a wavefront splitting type among interference measuring devices.
The interferometers often used for interference measurement using a laser include: Twyman-Green interferometer (ex., reference literature 1: Subfringe Interference Measurement Basic Theory, Optics 13 (1984) p.p. 55-65, or reference literature 2: Quantitative Phase Analysis in Electron Holographic Interferometry, Appl. Opt. 26 (1987) 377-382), Mach-Zehnder interferometer (reference literature 3: Interference Electron Microscopy by Means of Holography, Japan, J. Appl. Phys. 18 (1979) 2291-2294), further, Fizeau interferometer (reference literature 4: High Resolution Phase Measuring Laser Interferometric Microscope for Engineering Surface Metrology, SPIE 1009 (1988) 35-44), and the like. Any of the interferometers is of an amplitude splitting type which splits one beam into two beams, a beam transmitted through a semitransparent mirror and a beam reflected thereby.
On the other hand, also in the field of an electron beam, a study has been made on the measurement of not only the shape of an object but also the distribution of the electromagnetic field in the vicinity of a sample utilizing the phase information of an electron wave. The electron beam interferometer practically includes only an electron beam biprism (ex., reference literature 5: New Development in Electron Interference Measurement, Electron Microscopy 30 (1995) 113-120), reference literature 6: Japanese Laid-Open Patent Publication No. Hei 10-199464, and reference literature 7: Japanese Laid-Open Patent Publication No. Hei 11-40097). It is of a wavefront splitting type which spatially splits a beam into two beams, for example, a right-half beam and a left-half beam. There are not many cases where the wavefront splitting type is used for optical interference measurement.
In interference measurement, a beam changed in phase by a sample to be measured and a reference beam are allowed to interfere with each other to form an interference image. The distribution of phase changes due to the sample to be measured is examined from the resulting interference image. The information obtained from the distribution of phase changes varies according to the construction of the interference system. In the field of laser optics, the most common case is where the information is applied to the measurements of the surface precision and shape of the surface, unevenness of the thickness, and the like, of the sample to be measured. In the field of electron interference, the measurement of the distribution of electromagnetic field is also an important application other than the measurement of the shape of the sample to be measured.
As a method for calculating the distribution of phase changes from the interference image, for example, mention may be made of the following method. One interference image is inputted and stored into a calculating device via an image pickup element and an image capture board. This is mathematically Fourier transformed, so that there occur ±primary spectra corresponding to the basic interference fringes determined by the angle formed between two interfering luminous fluxes and the directions thereof with the center of the Fourier spectrum diagram as a center of point symmetry. The phase-changed components due to the sample are distributed around the + primary and − primary spectra, which are equivalent to each other. Therefore, one spectrum is selected with a window having a proper size to be Fourier inverse transformed. As a result, the distribution of phase is reproduced.
The phase distribution includes the tilt components due to the angle formed between the two luminous fluxes which have been allowed to interfere with each other. Therefore, the selected spectrum is shifted to the origin point, and then Fourier inverse transformed, or it is Fourier inverse transformed, and then the tilt component is corrected. As a result, it is possible to determine the distribution of phases changed by the sample.
The method most commonly used for a high-precision interference measurement is the fringe scanning method (also referred to as a phase shift method, in section 3.2 on page 58 of the reference literature 1). The detail of the measurement principle of this method is described on pages 58 to 59 of the reference literature 1, and hence a detailed description thereon is omitted. To be brief, the measurement principle is as follows.
With this method, in general, only the conditions for forming interference fringes are changed, so that the resulting interference image is recorded while successively shifting the relative phase difference between an object wave and a reference wave at an observing plane by a 1/M the wavelength (M is a positive integer of 3 or more). From the recorded M-interference-image group data, the distribution φ(x,y) of the phases changed by the sample is expressed as the following equation (1):                               ϕ          ⁡                      (                          x              ,              y                        )                          =                              tan                          -              1                                ⁡                      [                                                            ∑                                      m                    =                    1                                    M                                ⁢                                                      I                    ⁡                                          (                                              x                        ,                                                  y                          ;                          m                                                                    )                                                        ⁢                                      sin                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                           ⁢                          n                                                M                                            )                                                                                                                    ∑                                      m                    =                    1                                    M                                ⁢                                                      I                    ⁡                                          (                                              x                        ,                                                  y                          ;                          m                                                                    )                                                        ⁢                                      cos                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                           ⁢                          m                                                M                                            )                                                                                            ]                                              (        1        )            where I(x,y;m) denotes the intensity distribution of the interference image captured for the m-th time. The relative phase difference between the object wave and the reference wave is generally changed in the following manner. A reflecting mirror or a semitransparent mirror is micro-moved by a piezoelectrically driven stage, or the like, thereby to change the optical path length of the reference beam. This method is also used for electron interference. In this case, the relative phase difference between the object wave and the reference wave is changed in the following manner. Namely, an electron beam biprism is moved, or the tilt of the beam to be irradiated onto a sample to be measured is changed.
In the field of laser optics, high-precision interference measuring devices are mostly of a reflection type on the order of equal magnification, and there are less examples of microscopes of a reflection type (the reference literature 4). There are further less examples of transmission type microscopes, although there is the example of Mach-Zehnder interferometer using a Koster prism (reference literature 8: Quantitative measurement of a phase object by fringe scanning interference microscopy, Appl. Opt. 28 (1989) 1615-1617). In any of these examples, splitting of beams is accomplished based on the amplitude splitting type. In the field of electron beam, in most cases, the wavefront splitting type and transmission type microscopes are employed from the restriction of the interferometer.
Also in the field of laser optics, the configuration of a transmission type microinterferometer system based on the wavefront splitting mode has a large merit. With the transmission type microinterferometer system, although the beam transmitted through the sample is enlarged by the use of a lens system, the reference beam is also required to be enlarged simultaneously. With the transmission type microinterferometer system of the amplitude splitting mode, the two split luminous fluxes pass through largely different paths, and hence tend to be affected by vibration. Thus, a very large magnifying lens is required to be inserted, alternatively, the same magnifying systems are required to be inserted to their respective optical paths as in the reference literature 8. In contrast, with the wavefront splitting mode, the two luminous fluxes pass through almost the same paths, and hence they are less susceptible to vibration. Accordingly, only one system is required as the magnifying lens system.
In order to carry out the fringe scanning method with the interference system of the wavefront splitting type, the relative positional relationship between a sample image and interference fringes is required to be shifted on the observing plane. To do this, for example, the following methods are conceivable.    1. The wavefront splitting element is moved in the direction orthogonal to the wavefront splitting boundary;    2. The tilt of the exposure beam is changed in the direction orthogonal to the wavefront splitting boundary;    3. The refractive index of the wavefront splitting element is changed;    4. A phase modulation element (ex., liquid crystal plate) is inserted in at least one of the object wave or the reference wave to change the phase; and    5. When alignment is performed in the calculating device, the sample is moved with the interference conditions left unchanged.The first, second, and fifth methods can be readily applied to any of the laser interference system and the electron beam interference system. However, the third method and the fourth method are practically difficult to be applied to the laser interference system and the electron beam interference system, respectively.
FIG. 1 shows an example of a configuration of a wavefront splitting type fringe scanning laser interference measuring device. In this example, there is shown a method in which a biprism 5 which is a wavefront splitting element is moved, thereby to change the relative positional relationship between a sample image and interference fringes. A beam emitted from a coherent beam source (a laser in this case) 1 is converted to a parallel light by collimator lenses 2 and 3, and irradiated to a sample 10. When the sample 10 is small, the collimator lenses are not necessarily required. The transmission image of the sample 10 is formed on an observing plane 21 by using an objective lens 4. In this example, the image is formed directly on the image pickup surface of an image pickup element 20. The beam transmitted through the sample 10 (the portion of the dotted area in the figure) 11 has been changed in phase according to the distribution of the refractive index for the exposure beam in the sample. A wavefront splitting element in triangle pole (herein, also referred to as a biprism) 5 is placed at an appropriate position between the objective lens 4 and the observing plane 21. Thus, the beam transmitted through the sample 10 (hatching slanting downwardly to the right: generally referred to as an object wave) 12 passes through the focal point of the objective lens 4, and then, passes through the upper part of the biprism 5 to be deflected closer to an optical axis 13. Whereas, the beam passed through the part where there is no sample (hatching portion slanting upwardly to the right: generally referred to as a reference wave) 14 is deflected in the opposite direction. As a result, interference fringes are formed at the overlapping portion of both (crosshatching portion) 15. On the observing plane 21, there occur linear interference fringes in the sample-less portion. Whereas, there are observed interference fringes deviated from straight lines in proportional to the phase distribution of the transmission beam.
A reference numeral 30 denotes a monitor for image observation. It converts a signal from the image pickup element 20 into an image, and displays it. A reference numeral 50 denotes a calculating device, to which a monitor for a calculating device 60 is connected. Thus, it performs the operation and management of a laser interference system. A reference numeral 51 denotes an image capture board, which is an interface for capturing a signal from the monitor 30 for image observation into the calculating device 50. Incidentally, the monitor 30 for image observation is capable of also serving as the monitor 60 for a calculating device. On the monitor for image observation 30, as with the case on the observing plane 20, there occur linear interference fringes in the sample-less portion, while there are observed interference fringes shifted in accordance with the phase distribution of the transmission beam in the sample-including portion.
In order to carry out the fringe scanning interferometry, herein, a signal is sent to a micro-movement control device 40 in response to an instruction via the calculating device 50 from an observer, so that a micro-movement control mechanism 41 by a piezo element is micro-moved. Accordingly, the biprism 5 is moved in the direction orthogonal to both the optical axis 13 and the wavefront splitting boundary of the biprism 5, i.e., in the upward or downward direction in the figure. For example, when the biprism 5 is micro-moved upwardly, the object wave 12 passes through the thicker portion of glass of the biprism 5, and hence it is delayed in phase. Whereas, the reference wave 14 passes through the thinner portion, and hence it is advanced in phase. FIG. 2 shows the manner in which the object wave and the reference wave interfere with each other in this case.
The laser light indicated by an arrow A is the object wave 12 transmitted through the sample 10. Each of the wavefronts 121, 122, . . . has an uneven shape in accordance with the distribution of refractive index in the sample 10. On the other hand, the laser light indicated by an arrow B is a reference plane wave, and the wavefronts are indicated by a line group 131, 132, . . . in the figure. When the laser light A and the laser light B tilted to the left and right, respectively, each at an angle of θ from the optical axis 13 interfere with each other, they reinforce each other at the region where the left and right wavefronts cross each other, resulting in a higher intensity. Whereas, they cancel each other at the region where the left and right wavefronts are superimposed in such a manner as to be shifted from each other by a half distance, resulting in a lower intensity. As a result, there occur interference fringes with the intensity distribution as indicated by a solid curved line 22.
At the regions where there is not present the sample 10 as in the opposite left and right edges of FIG. 2, there is the relationship expressed by the following equation (2) between the distance d between interference fringes, and the wavelength λ and the tilt θ of the laser light, and the relationship can be expressed as the equation (3) because the θ is generally very small.2d sin θ=λ  (2)                     d        =                  λ                      2            ⁢            θ                                              (        3        )            
Such interference fringes are determined by the interference system, and hence referred to as basic interference fringes or carrier interference fringes. On the other hand, the interference fringes in the region where the light rays have transmitted through the sample are not in straight lines, and locally shifted in distance and direction from the basic interference fringes in accordance with the phase changes.
Herein, a consideration will be given to the case where the laser light B of the reference wave 13 has been slightly advanced in phase. The wavefronts have moved to the positions respectively indicated by broken lines 131′, 132′, . . . and each of the wavefronts crosses the different portion of the object wave 12. Accordingly, the resulting interference fringes are shifted as indicated by a broken curved line 22′. The movement of the interference fringes is determined by the relative positional relationship between the object wave 12 and the reference wave 13, regardless of whether the object wave 12, or both the object wave 12 and the reference wave 13 are advanced or delayed in phase. Even when the object wave 12 is advanced or delayed in phase, the tilt of the beam due to the biprism 5 is constant, so that the image of the sample does not move.
Thus, every time an interference image wherein the basic interference fringes have been shifted by 1/M (M: a positive integer of 3 or more) of the distance d is formed, the resulting interference image is captured into the calculating device 50 via the image pickup element 20 and the image capture board 51. A group of M interference images thus captured are sequentially arranged, indicating that the intensity of the laser light at a given one point in each of the images changes in accordance with the sine curve. FIG. 3 schematically shows this state for M=3, i.e., for three interference images M1, M2, and M3. The amount of phase change is plotted on the abscissa, and the luminance of the laser light is plotted on the ordinate, thus showing the relationship with respective interference images. The reason for limiting the value of M to 3 or more is that data of 3 points at minimum is required for determining the sine curve on one point. The brightness of one point in the first interference image may start from the peak, or halfway in the valley according to the position. The phase value measured from the origin point of the sine curve determined for the point corresponds to the phase value of the laser light transmitted through the point. Therefore, if this value is determined for each point in the interference images, it is possible to determine the phase distribution due to the sample.
Such a way to determine the phase distribution can be mathematically expressed as the following equation (4), slightly different in description from the foregoing equation (1) due to the presence of the basic interference fringes:                               {                                                    2                ⁢                π                ⁢                                                                   ⁢                x                            d                        +                          ϕ              ⁡                              (                                  x                  ,                  y                                )                                              }                =                              tan                          -              1                                ⁡                      [                                                            ∑                                      m                    =                    1                                    M                                ⁢                                                      I                    ⁡                                          (                                              x                        ,                                                  y                          ;                          m                                                                    )                                                        ⁢                                      sin                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                           ⁢                          m                                                M                                            )                                                                                                                    ∑                                      m                    =                    1                                    M                                ⁢                                                      I                    ⁡                                          (                                              x                        ,                                                  y                          ;                          m                                                                    )                                                        ⁢                                      cos                    ⁡                                          (                                                                        2                          ⁢                          π                          ⁢                                                                                                           ⁢                          m                                                M                                            )                                                                                            ]                                              (        4        )            where d denotes the distance between the basic interference fringes, of which the direction is matched to the direction of y axis. The first term of the left side is the linear tilt resulting from the interference of two tilted beams. Therefore, it is the already known amount, and hence it is easy to remove by calculation. Incidentally, the measurement not using the fringe scanning method is also possible. In such a case, one interference image may be captured into the calculating device 50 via the image pickup element 20 and the image capture board 51, and calculated by the foregoing Fourier transform method.
The phase distribution due to the sample determined by the transmission type microscope is the refractive index distribution for the laser interference system, and the sample thickness distribution, the internal potential distribution (corresponding to the refractive index distribution), and the distribution of electromagnetic field inside and outside the sample for the electron beam interference system.
FIG. 4 shows a fringe scanning electron beam interference device. Only an exposure optical system, a sample to be measured, and an electron beam biprism are shown for simplification. A vacuum container system including therein these components, a magnifying lens system, a power source system, and the like are not shown. Further, devices necessary for the measurement such as an image pickup element and a calculating device are the same as those in the laser interference measuring device, and hence they are omitted.
A reference numeral 71 denotes an electron beam source, and a reference numeral 72 is an electron beam emitted therefrom. The electron beam 72 emitted from the electron beam source 71 is converted to a nearly parallel beam through an exposure lens (exposure lens system) 73, and irradiated to a sample 74. The wavefront of the electron beam 72 is indicated by a solid line. The wavefront of the electron beam 72 is changed in phase due to the distribution of thickness of the sample 74 and the distribution of electromagnetic field inside and outside the sample upon passing through the sample 74, resulting in an uneven wavefront. The wavefront splitting element for electron interference is generally only an electron beam biprism. The electron beam biprism is made up of oppositely disposed electrodes 75 and 76, and a thin electrode 77 at the midpoint therebetween. The thin electrode 77 has a function of drawing electron beams passing through its opposite sides, and superimposing the beams in the region therebeneath by the application with a voltage of about +100 V. Therefore, if the sample is placed in either half of the electron beam path, the interference image of the sample-transmitted wave and the reference wave is formed on an observing plane 78. If the electron beam biprism is moved slightly rightward as indicated by an arrow, the difference in progressing speed is caused between the wavefronts of the object wave and the reference wave as indicated by broken lines in the figure. As a result, the fringes in the interference image are moved. However, even if the electron beam biprism is moved, the image of the sample is not moved because the tilt angle is constant. Therefore, the electron beam interference measurement can also be carried out in the same manner as with the laser interference. The phase distribution changed due to the sample can be measured by using the fringe scanning method, or the Fourier transform method when the electron beam biprism is not moved. Incidentally, for the movement of the electron beam biprism, a piezo element, a stepping motor, or the like is used as with the laser interference measuring device, but it is not shown.